Order of magnitude

A order of magnitude allows a simplified and synthetic representation of a physical Grandeur. They are practical to communicate on sizes of the infinitely great or infinitely small.

In general, an order of magnitude is a range of values which goes from a tenth to ten times the rated quantity (i.e. stated size). Thus, if it is said that

“the order of magnitude is of one meter”
that means that the length of the object is between 10 cm and 10 Mr. Of other times, one considers smaller forks, such as for example between half and the double of the value (thus here between 50 cm and 2 m).

In extreme cases, the exact order of magnitude is for a positive reality X, there: = log X; and often E, or E indicates the whole part of Y.

In a general way, the width of the fork depends on the way in which the person thinks the phenomenon. Thus, a temperature “about 20  °C” will not have the same significance for a person living in a country with weak or great thermal amplitude, or according to the season to which the person refers; a French who thinks one day sunny of spring will consider a fork of 15 with 25  °C, while a person thinking of the summer will have a fork of 18 with 30  °C at the head.

This inaccuracy is in general not awkward, since one is not interested in the exact value, one wants right knowledge if two sizes are comparable or not.

Knowledge of about size of a phenomenon makes it possible to check that the result of a calculation is coherent, therefore that one did not make a big mistake. Thus, if the result of a calculation is the distance between a French city and a étatsunienne city, one expects to have a result of several thousands of kilometers; a result of a few hundreds kilometers, or contrary to 10  000 kilometers, will appear doubtful.

The very important concept of literal Order of magnitude is relating to the theory of the dimensional Analyze and the Théorème pi

Prefixes of the units

The basic units of the international system are modified by prefixes. A prefixed unit can thus indicate an order of magnitude, one can say for example

“the Fréquence used in the Bande FM is about the hundred Méga hertz”
(in France, this band extends from 88 to 108 MHz).

Here the current prefixes used for the orders of magnitude:

Yotta 1024
Zetta 1021
Exa 1018 ( example: 1 EHz = 1018 Hz )
Péta 1015 ( example: 1 PHz = 1015 Hz )
Téra 1012 (thousand billion; example: 1 THz = 1012 Hz
Giga 109 (a Billion; example: 1 GHz = 109 Hz )
Méga 106 (a Million; example: 1 MHz = 106 Hz )

Kilo 103 ( example: 1  km = 1  000 m )

Hecto 102 ( example: 1 hm = 100 m )
Decaf 101 ( example: 1 prejudice = 10 m )

Déci 10-1 ( example: 1 DM = 0,1 m )

Centi 10-2 ( example: 1 cm = 0,01 m )
Milli 10-3 ( example: 1 mm = 0,001 m )

micro 10-6 (one millionth; example: 1 µs = 10 -6 S )

Nano 10-9 (a billionth; example: 1 NS = 10 -9 S )
Pico 10-12
Femto 10-15
Atto 10-18
Zepto 10-21
Yocto 10-24

The engineers, the scientists and the mathematicians have as a use to use orders of magnitude which are powers of 10 multiple of 3 ( nano, micro, milli, kilo, méga, giga… )

Orders of magnitude of various quantities

In the following table, the following quantities are placed side by side in the same line:

  • the length and the approximate time used by the light to cross this length

  • the surface of a square and the length on a side
  • the volume of a cube and the surface of one of its faces
  • mass of water and its volume to 4 degrees Celsius or 277,15 K

* Each time shown is related to this time. However, so that the light crosses the corresponding distance, 3 times are needed shown time.

** They are the units standards, but the table uses varied units, which can make the reading more complicated.

Units used in the table

This table uses units and prefixes commonly used:
  • Time:
    • Femtoseconde (fs)
    • Picosecond (PS)
    • Nanosecond (NS)
    • Microsecond (µs)
    • Millisecond (ms)
    • second (S)
    • hour (H)
    • Day (J)
    • year (year)
  • Length:
  • Surface:
  • Mass:
  • Volume:
  • Energy:
    • milliélectronvolt (meV),
    • electronvolt (eV)
    • mégaélectronvolt (MeV)
    • gigaélectronvolt (GeV)
    • téraélectronvolt (TeV)
    • Joule (J)
    • kilowatt-hour kWh
    • mégawattheure MWh
    • gigawattheure GWh
  • Temperature:
    • nanokelvin (nK)
    • microkelvin (µK)
    • millikelvin (mK)
    • Kelvin (K)

See too

Related articles

External bonds

  • Powers of 10, a graph animated illustrating the orders of magnitude on the basis of a sight of the Galaxy to 1023 meters and while finishing with subatomic particles with 10-16 meters, inspired of the film Powers off Ten (1977)

  • Powers off Ten, original film of Charles and Ray Eames

Simple: Order off magnitude

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